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The proof-of-work algorithm makes the bitcoin miners choose a value for a set of fields in the new blocks header, such that the hash of the generated block satisfies a difficulty target. This criteria is the number of leading zeroes in the hash of the block.
This is a frequently repeated misunderstanding.
The criteria is that the value of the hash be less than a particular target value. The fact that this value is currently significantly less than 2256 means that there will be several 0's in the beginning of the hash, but the zeros are not the criteria. If they were, then difficulty would have to double (or half) every time it changed and that wouldn't leave room to keep the average close to 10 minutes.
Thanks DannyHamilton :-), I have fixed it.
